On January $1,$ Year $1,$ Chen Company issued $$300,000$ of five$-$year, $6$ percent bonds at $101.$ Interest is payable annually on December $31.$ The premium is amortized using the straight$-$line method.

Determined the amount of cash proceeds received by Chen Company on January $1,$ Year $1.$

Calculate the amount of interest expense as of December $31,$ Year $2.$

What is the carrying value of the bond liability as of December $31,$ Year $2?$